Scalp surface estimation and head registration using sparse sampling and 3D statistical models

Registering the head and estimating the scalp surface are important for various biomedical procedures, including those using neuronavigation to localize brain stimulation or recording. However, neuronavigation systems rely on manually-identified fiducial head targets and often require a patient-specific MRI for accurate registration, limiting adoption. We propose a practical technique capable of inferring the scalp shape and use it to accurately register the subject’s head. Our method does not require anatomical landmark annotation or an individual MRI scan, yet achieves accurate registration of the subject’s head and estimation of its surface. The scalp shape is estimated from surface samples easily acquired using existing pointer tools, and registration exploits statistical head model priors. Our method allows for the acquisition of non-trivial shapes from a limited number of data points while leveraging their object class priors, surpassing the accuracy of common reconstruction and registration methods using the same tools. The proposed approach is evaluated in a virtual study with head MRI data from 1152 subjects, achieving an average reconstruction root-mean-square error of 2.95 mm, which outperforms a common neuronavigation technique by 2.70 mm. We also characterize the error under different conditions and provide guidelines for efficient sampling. Furthermore, we demonstrate and validate the proposed method on data from 50 subjects collected with conventional neuronavigation tools and setup, obtaining an average root-mean-square error of 2.89 mm; adding landmark-based registration improves this error to 2.63 mm. The simulation and experimental results support the proposed method’s effectiveness with or without landmark annotation, highlighting its broad applicability.

As mentioned in Section 3.1.2,some images are excluded from the MRI datasets due to technical issues and unusual image artifacts that distort significantly the head surface.Examples of such images can be found in Some of the segmented head meshes we considered valid during the preprocessing stage include artifacts in the form of excessive parts of the inner skull and planes in the skull cavity.These might later affect alignment with the statistical head model or the cropping of the scalp shape.In some of the valid scans, subject heads are found at a variety of different angles, or include parts of the headrest and chin support that some subjects used during the scan (see Figure S.3).Such spurious objects and artifacts are removed by detecting mesh planar facets and removing vertices found in their 3D minimum bounding box.Subject head surfaces are not smoothed or processed in any way that reduces their fidelity to the original and true shape.In order to fix the angle of the MRI image head, we rotate it such that the spatial coordinate of the tip of the nose is aligned with the head points median value along the  axis (horizontal direction).Most of the subject images we consider valid still include some unusual deformities, mainly in the form of back and head support artifacts, missing parts of the ears, and cropped noses.These do not affect the virtual experiments carried out in this paper.

A.2. Joint optimization details
We compute the initialization point by performing a coarse alignment without using any facial data, as often done during registration (see Section 2).Instead, we leverage the head's coarse shape, as captured by sampled data.First, we transform the 3DMM mean shape to match the general proportions of the samples representing the subject's head, by uniformly scaling it by   such that its span across the  axis will match those of the subject's samples We take into account the subjects' missing ears, usually not being included in the samples representing the head surface, by adjusting the 3DMM span across the  axis, and multiplying it by a factor of  = 0.9, based on empirical observations.We also translate the 3DMM mean shape by  so that its point with the highest value over the vertical  axis aligns with the highest point among the subject samples This is due to the relatively low variation in values at the top part of the scalp.
During the joint optimization procedure, we do not enforce the spatial positions of sampled vertices nor their relative positions, but extrapolate using them.
Figure S.1.Other images are included although having certain image artifacts, considering these do not disrupt the head anatomy (see examples in Figure S.2).

Figure S. 1 :
Figure S.1: Examples of subjects excluded due to technical issues and image artifacts that impair the integrity of the head surface (red ellipses).Top row shows IXI dataset examples.Bottom row shows ADNI dataset examples.

Figure S. 2 :
Figure S.2: Examples of subjects included in this study while having slight image artifacts over the head surface (red ellipses).Top row shows IXI dataset examples.Bottom row shows ADNI dataset examples.

Figure S. 3 :
Figure S.3: Examples of the effects of image cleaning we performed.Top row shows images before the data cleaning step.Bottom row shows the corresponding images after they have been inspected and cleaned.Red ellipses in the three leftmost images in the top row identify artifacts or external objects.The rightmost images exemplify the step of image angle correction implemented during cleaning.

Figure S. 4 :
Figure S.4: Illustration of head sections as partitioned when using non-random sampling strategies, with n=9.Grayscale colors demonstrate the internal partition described in Section 3.3.2.